1. Field of the Invention
This invention relates to sensors used to align mirror segments of a segmented telescope. More specifically, the invention is an achromatic shearing phase sensor that can be used in the detection of out-of-plane alignment errors between segments of a segmented telescope's mirrors.
2. Description of the Related Art
In order to reduce some of the mechanical and financial burdens associated with a large aperture telescope, multiple mirror or segmented telescopes have found a place in the family of space-based and Earth-based optics. The difficulty in using a segmented telescope is that the mirror segments must be aligned such that they perform as a contiguous surface. When this is accomplished, two benefits are obtained. First, the energy from each segment coherently sums at the segments' focus. Second, the higher spatial frequency information from the source is preserved, i.e., spatial frequency ξ∝1/x where x is the largest spatial dimension of the telescope's aperture. The result is a much brighter and much smaller image of each point of the source.
To behave as a contiguous surface, each mirror segment must produce an image at the same place in all three spatial dimensions. Alignment in the x and y dimensions perpendicular to the direction of propagation, is relatively straightforward. This task can be achieved by direct measurement of the irradiance from a particular segment. The third dimension (i.e., z-axis) is more difficult to align because it involves measurement of the phase of a wavefront. To achieve this measurement, the phase is typically inferred from irradiance patterns.
The alignment of a mirror segment's wavefronts (or phase alignment) must be accurate to a small fraction of the operation wavelength of light for coherent imagery to occur. Measurement of the wavefront's phase must be even more precise to achieve sufficient alignment for a given application.
Phase alignment of most segmented telescopes can be achieved in stages. The first stage or course alignment phases the mirror segments to within a few wavelengths using a large capture range sensor that can be somewhat inaccurate. The next stage finely aligns the system to a fraction of the operating wavelength using a sensor with a comparatively small capture range but very good accuracy. Finally, alignment can be maintained by a third sensor that is fast and efficient. Combinations of wavefront sensing techniques, such as a Shack-Hartmann and a wavefront curvature sensor, have been investigated for some extra large telescope (ELT) designs. Since phasing may be achieved in many stages by many sensors, the attributes of a useful sensor varies. The application of the sensor to a telescope that is space-based looking out, spaced-based looking in, or Earth-based, can change the sensor's requirements dramatically.
Currently, there are five categories of phasing techniques used to address the segmented telescope phasing problem. The first technique is a mechanical approach commonly represented by inductive or capacitive sensors (i.e., edge sensors as they are known) located on the structure of the segments. The second technique is the accurate but sometimes mathematically complex phase retrieval techniques. Related to the phase retrieval techniques are the third and fourth techniques known as curvature sensing techniques and image metric techniques, respectively. The fifth technique utilizes adjacent segment interferometry.
Mechanical edge sensors are typically inductive coil or capacitive sensors located on the structure of a segment for measuring the position of one segment relative to an adjacent segment. However, the physical size of the edge sensors and spacing therebetween limits the capture range thereof. Further, edge sensors and their measurements can be affected by physical changes to the mirror segment's edges induced by environmental conditions. Thus, edge sensors are not well suited to long-term use where the physical properties of a segmented telescope may change.
Phase retrieval techniques are based on what is known as the phase diversity concept. The phase diversity method utilizes two or more simultaneous, monochromatic images (i.e., one in-focus and one out-of-focus) to calculate the wavefront at the telescope's pupil plane. The in-focus image is mathematically described as the convolution of the point spread function with the object. The out-of-focus image is similar except there is a known defocus term in the second point spread function. Since the defocus term is well quantified, the point spread function of the optical system and the object irradiance distribution can be mathematically estimated. In general, phase diversity techniques are quite complex and time consuming making them impractical for use with dynamic telescopes or telescopes that drift at a faster rate than the time it takes for the phase diversity calculation to be completed. (More recently, modified phase diversity techniques, i.e., phase-diverse phase retrieval and phase diversity wavefront sensing, have been proposed. These updated techniques somewhat simplify the mathematics involved by removing one or more Fourier transforms required.) Phase retrieval techniques are also somewhat limited in that they generally must be used with point sources, although an extended source could be used if sufficient spatial information is provided. However, use with a broadband source requires a substantial amount of sensing and processing sophistication.
Similar to phase retrieval techniques are curvature sensing techniques that also compare two images, one before focus and one after focus, to compute the curvature of the wavefront. Variations on this concept have been applied to segmented telescopes by a number of research groups. For example, phase discontinuity sensing is a curvature sensing technique that compares two images of a point source formed by a segmented mirror. The images are far enough away from the focal plane that each of the mirrors are distinguishable from the others. The after-focus image is rotated 180° to compensate for the inversion upon going through an image plane. The two images are then subtracted pixel-by-pixel. The difference image is compared to a library of template difference images. The comparison correlation coefficient varies linearly with (mirror segment) piston error. When a segment is aligned appropriately, the images before and after focus are identical and the difference irradiance distribution is zero. When this occurs, the correlation coefficient between the measured image and the template image will also be zero. As the mirror becomes misaligned, the images change relative to each other and the difference irradiance increases as does the correlation coefficient. The correlation coefficient continues to increase until the piston exceeds λ/8 where it begins to decline. While the curvature sensing technique utilizes a fast algorithm for analyzing the piston errors of a segmented telescope, it is an iterative process and has a limited capture range.
Image metric techniques are based upon calculating a single number (or a few numbers) from the image of a segmented telescope. The number or metric is recalculated after an adjustment has been made to the telescope. If the new calculation is improved compared to the original, the adjustment to the telescope is maintained as the new configuration. There are many different metrics to indicate improved alignment such as maximum irradiance, Strehl ratio, and total encircled energy. However, image metric techniques can only optimize alignment with regard to the particular metric being employed which, typically, is only indicative of one aspect of alignment. Thus, image metric techniques may not provide the necessary information for overall mirror segment alignment.
Adjacent segment interferometry techniques compare the piston positions of two adjacent mirror segments using interferometry methods. The relative piston positions from each pair is reported by a sensing system to an algorithm that calculates the optimum mirror alignment. The sensing system can be a phasing camera system (PCS) that analyzes the interference pattern generated by a mask having small circular (or square) apertures located at each of the telescope's inter-segment edges when the mask is placed over the telescope's image. The size of each aperture is chosen to be smaller than the Fried parameter, which is the atmospheric turbulence coherence length.
For computational simplicity, the interference pattern transmitted through the apertures is compared to a simulated set of templates. The templates are irradiance patterns that would be observed if the phase difference between the two segments (each filling one half of the circular sub-aperture) were translated from in-phase to out-of-phase, then back in-phase in small steps.
The technique is first performed using broadband sources and then performed using narrowband sources for increased accuracy. That is, the measured data are first collected using a series of broadband sources. Each consecutive source has a broader band (i.e., a shorter coherence length) than the previous source to ultimately find the absolute phase position of the segments. For each source, multiple measurements are collected as one segment scans through a distance corresponding to the coherence length of the source. When a particular measured interference pattern correlates well with a template, this indicates that the segments are positioned within the coherence length of the source. The scanned mirror is then returned to the appropriate position where interference occurred. This process is applied with successfully broader sources to “walk” the mirror segments into alignment.
After achieving segment alignment to within one wavelength phase difference using broadband sources, a similar process is performed using narrowband sources. Specifically, a monochromatic source is used to generate the interference pattern data set. This data set is also compared with the original templates to find the absolute phase alignment position for each mirror as opposed to the degree of interference. After the two images with the highest correlation coefficient are determined, a quadratic interpolation is used to achieve finer resolution of piston measurement. However, the algorithm used for narrowband phasing is limited in its accuracy.
Another adaptive segment interferometry technique uses a dispersed fringe sensor (DFS). Like the PCS method, DFS uses a mask having an array of apertures aligned with the inter-segment edges of the telescope to compare the irradiance from adjacent segments. The apertures are rectangular with the longer dimension being parallel to the gap between mirror segments. In DFS, the transmitted irradiance from two adjacent mirrors interfere. A dispersing optic such as a prism or diffraction grating separates the interference pattern generated by a white light source into a series of monochromatic fringe patterns perpendicular to the aperture orientation. Along the vertical axis of the interference pattern, the wavelength is constant, while along the horizontal axis, the wavelength varies. Each vertical cross-section of the pattern indicates the piston difference of the two mirrors as measured by the corresponding wavelength. The period of the fringe pattern along the wavelength axis, measured as a function of space, is used to calculate the piston difference between two segments of a telescope. The sign of the error is determined by slightly moving one element and then re-measuring the phase difference. The accuracy of the DFS technique reduces as the piston difference approaches zero and the period of the overall pattern becomes large or infinite.
More importantly, both of the above-described mask-based sensors (i.e., PCS and DFS) are limited to measuring very small edge portions of each mirror segment. As a result, information generated by these sensors is “silent” with respect to any mirror segment deformations which can be critical in segmented telescope alignment.